Range Sum Query 2D - Mutable

Question

Given a 2D matrix, find the sum of the elements inside the rectangle defined by (row1, col1), (row2, col2).

Example:

``````Given matrix = [
[3, 0, 1, 4, 2],
[5, 6, 3, 2, 1],
[1, 2, 0, 1, 5],
[4, 1, 0, 1, 7],
[1, 0, 3, 0, 5]
]

sumRegion(2, 1, 4, 3) -> 8
sumRegion(1, 1, 2, 2) -> 11
sumRegion(1, 2, 2, 4) -> 12
``````

Note:

1. You may assume that the matrix does not change.
2. There are many calls to sumRegion function.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

Solution

binary indexed tree

``````class NumMatrix {
vector<vector<int>> tree;
vector<vector<int>> ma;
public:
NumMatrix(vector<vector<int>> &matrix) {
int n = matrix.size();
int m = n == 0 ? 0 : matrix[0].size();
if (n == 0 || m == 0) {
return ;
}

tree = vector<vector<int>>(n + 1, vector<int>(m + 1, 0));
ma = vector<vector<int>>(n, vector<int>(m, 0));
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
update(i, j, matrix[i][j]);
}
}
}

void update(int row, int col, int val) {
int delta = val - ma[row][col];
ma[row][col] = val;
for (int i = row + 1; i <= ma.size(); i += i & (-i)) {
for (int j = col + 1; j <= ma[0].size(); j += j & (-j)) {
tree[i][j] += delta;
}
//for (int j = col + 1; j > 0; j -= j & (-j)) {
//    sol += tree[i][j];
//}
}
return sol;
}

int sumRegion(int row1, int col1, int row2, int col2) {

}
};

// Your NumMatrix object will be instantiated and called as such:
// NumMatrix numMatrix(matrix);
// numMatrix.sumRegion(0, 1, 2, 3);
// numMatrix.update(1, 1, 10);
// numMatrix.sumRegion(1, 2, 3, 4);
``````

another implementation

``````class NumMatrix {
vector<vector<int>> rowSums;
vector<vector<int>> ma;
public:
NumMatrix(vector<vector<int>> &matrix) {
int n = matrix.size();
int m = (n == 0) ? 0 : matrix[0].size();
if (n == 0 || m == 0) {
return;
}
ma = matrix;
rowSums = vector<vector<int>>(n, vector<int>(m + 1, 0));
for (int i = 0; i < n; i++) {
for (int j = 1; j <= m; j++) {
rowSums[i][j] = rowSums[i][j - 1] + matrix[i][j - 1];
}
}
}

void update(int row, int col, int val) {
for (int i = col + 1; i <= ma[0].size(); i++) {
rowSums[row][i] += (-ma[row][col] + val);
}
ma[row][col] = val;
}

int sumRegion(int row1, int col1, int row2, int col2) {
int sol = 0;
for (int i = row1; i <= row2; i++) {
sol += (rowSums[i][col2 + 1] - rowSums[i][col1]);
}
return sol;
}
};
``````